According to the use of binomial expansion, the approximate value of √3 is found by applying the infinite sum √3 = 1 + (1 /2) · 2 - (1 / 8) · 2² + (1 / 16) · 2³ - (5 / 128) · 2⁴ + (7 / 256) · 2⁵ - (21 / 1024) · 2⁶ + (33 / 2048) · 2⁷ - (429 / 32768) · 2⁸ +...
An acceptable result cannot be found manually for it requires a <em>high</em> number of elements, with the help of a solver we find that the <em>approximate</em> value of √3 is 1.732.
<h3>How to approximate the value of a irrational number by binomial theorem</h3>
Binomial theorem offers a formula to find the <em>analytical</em> form of the power of a binomial of the form (a + b)ⁿ:
(1)
Where:
- a, b - Constants of the binomial.
- n - Grade of the power binomial.
- k - Index of the k-th element of the power binomial.
If we know that a = 1, b = 2 and n = 1 / 2, then an approximate expression for the square root is:
√3 = 1 + (1 /2) · 2 - (1 / 8) · 2² + (1 / 16) · 2³ - (5 / 128) · 2⁴ + (7 / 256) · 2⁵ - (21 / 1024) · 2⁶ + (33 / 2048) · 2⁷ - (429 / 32768) · 2⁸ +...
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Answer:
A.96.25 steps. B. Approximately 37 steps shorter
Step-by-step explanation:
From Pythagoras theory,
Hyp² = Adj² + Opp²
Hyp² = 52² + 81²
Hyp² = 2704 + 6561
Hyp² = 9265
Hyp = √9265
Hyp = 96.25 steps
= 81 + 52 = 133 - 96.25
= 36.75 or approximately 37 steps shorter
Answer:
24.6
Step-by-step explanation:
you multiply them all by two then add them together. :P
Answer:
Answer is 910
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Step-by-step explanation:
A construction is a geometric drawing that uses a limited set of tools, usually a compass and straightedge. You can ... compass and straightedge (a ruler without marks) to construct a segment that is congruent to a given segment, and an ... CRITICAL THINKING: Describe how you could use a compass and a straightedge to.
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